Block #308,107

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 10:30:38 PM · Difficulty 9.9944 · 6,499,969 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

bb1924a3c9c09d14c424f2f951bb3f9bb17133057027ec4b22776c96a744a2d7

View on Chainz ↗

Height

#308,107

Difficulty

9.994403

Transactions

Size

1.18 KB

Version

Bits

09fe9138

Nonce

30,950

Timestamp

12/12/2013, 10:30:38 PM

Confirmations

6,499,969

Mined by

⛏️ aR9AYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

1600e1ace0af984b919d4bf9b1e7c5c11eb7f419b3907bca7d76c0a8de3d95bf

Transactions (1)

Coinbase1600e1ace0af98…76c0a8de3d95bf

1 in → 31 out9.9800 XPM1.09 KB

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AXES7e6y…YiapChVv Ae6gEbs5…m5Mn8oYw AMbCuLHZ…WSoStwkc

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.422 × 10⁹⁴(95-digit number)

14227445428746920345…79596570385755750399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.422 × 10⁹⁴(95-digit number)

14227445428746920345…79596570385755750399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.422 × 10⁹⁴(95-digit number)

14227445428746920345…79596570385755750401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.845 × 10⁹⁴(95-digit number)

28454890857493840691…59193140771511500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.845 × 10⁹⁴(95-digit number)

28454890857493840691…59193140771511500801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.690 × 10⁹⁴(95-digit number)

56909781714987681383…18386281543023001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.690 × 10⁹⁴(95-digit number)

56909781714987681383…18386281543023001601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.138 × 10⁹⁵(96-digit number)

11381956342997536276…36772563086046003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.138 × 10⁹⁵(96-digit number)

11381956342997536276…36772563086046003201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.276 × 10⁹⁵(96-digit number)

22763912685995072553…73545126172092006399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #308,107

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